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<div class="header">
  <div class="headertitle"><div class="title">ECEFtoLLA.hpp</div></div>
</div><!--header-->
<div class="contents">
<a href="_e_c_e_fto_l_l_a_8hpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span> </div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="preprocessor">#pragma once</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span> </div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span> </div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span><span class="preprocessor">#include &quot;<a class="code" href="_coordinates_2_reference_frames_2_constants_8hpp.html">NumCpp/Coordinates/ReferenceFrames/Constants.hpp</a>&quot;</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="preprocessor">#include &quot;<a class="code" href="_e_c_e_f_8hpp.html">NumCpp/Coordinates/ReferenceFrames/ECEF.hpp</a>&quot;</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span><span class="preprocessor">#include &quot;<a class="code" href="_l_l_a_8hpp.html">NumCpp/Coordinates/ReferenceFrames/LLA.hpp</a>&quot;</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span><span class="preprocessor">#include &quot;<a class="code" href="_core_2_constants_8hpp.html">NumCpp/Core/Constants.hpp</a>&quot;</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span><span class="preprocessor">#include &quot;<a class="code" href="sign_8hpp.html">NumCpp/Functions/sign.hpp</a>&quot;</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="preprocessor">#include &quot;<a class="code" href="sqr_8hpp.html">NumCpp/Utils/sqr.hpp</a>&quot;</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span> </div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespacenc_1_1coordinates_1_1transforms.html">nc::coordinates::transforms</a></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>{</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"><a class="line" href="namespacenc_1_1coordinates_1_1transforms.html#ae5b0b317df7fc82c1a6467aa14ac37d4">   49</a></span>    [[nodiscard]] <span class="keyword">inline</span> <a class="code hl_class" href="classnc_1_1coordinates_1_1reference__frames_1_1_l_l_a.html">reference_frames::LLA</a> <a class="code hl_function" href="namespacenc_1_1coordinates_1_1transforms.html#ae5b0b317df7fc82c1a6467aa14ac37d4">ECEFtoLLA</a>(<span class="keyword">const</span> <a class="code hl_class" href="classnc_1_1coordinates_1_1reference__frames_1_1_e_c_e_f.html">reference_frames::ECEF</a>&amp; ecef, <span class="keywordtype">double</span> tol = 1<a class="code hl_variable" href="namespacenc_1_1constants.html#aebabe96d6c2be3df3d71922b399e24c7">e</a>-8) noexcept</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    {</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        <span class="keyword">constexpr</span> <span class="keywordtype">int</span>  MAX_ITER = 10;</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>        <span class="keyword">constexpr</span> <span class="keyword">auto</span> E_SQR    = 1. - <a class="code hl_function" href="namespacenc_1_1utils.html#ae792e10a24b7e5b8291a6c31a28a4512">utils::sqr</a>(<a class="code hl_variable" href="namespacenc_1_1coordinates_1_1reference__frames_1_1constants.html#ac759daa1c17c9d6cc404787d56b115ac">reference_frames::constants::EARTH_POLAR_RADIUS</a> /</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>                                               <a class="code hl_variable" href="namespacenc_1_1coordinates_1_1reference__frames_1_1constants.html#ace19ddeea3737fe42ad60256f310feaa">reference_frames::constants::EARTH_EQUATORIAL_RADIUS</a>);</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span> </div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>        <span class="keyword">const</span> <span class="keyword">auto</span> p   = <a class="code hl_function" href="namespacenc.html#a4648674053cd83851d9549bbcc7a8481">std::hypot</a>(ecef.<a class="code hl_variable" href="classnc_1_1coordinates_1_1_cartesian.html#add44d8cd4ee04ef61120fc0c0d12e550">x</a>, ecef.<a class="code hl_variable" href="classnc_1_1coordinates_1_1_cartesian.html#ac77a08a542ba4d873c0a86047b25953d">y</a>);</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>        <span class="keyword">const</span> <span class="keyword">auto</span> lon = std::atan2(ecef.<a class="code hl_variable" href="classnc_1_1coordinates_1_1_cartesian.html#ac77a08a542ba4d873c0a86047b25953d">y</a>, ecef.<a class="code hl_variable" href="classnc_1_1coordinates_1_1_cartesian.html#add44d8cd4ee04ef61120fc0c0d12e550">x</a>);</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span> </div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>        <span class="keywordtype">double</span> alt = 0.0;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>        <span class="keywordtype">double</span> lat = 0.0;</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span> </div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        <span class="keywordflow">if</span> (p &lt; tol)</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        {</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>            lat = <a class="code hl_function" href="namespacenc.html#a4a5d98f334e0b50a3cf9c2718485e5e9">sign</a>(ecef.<a class="code hl_variable" href="classnc_1_1coordinates_1_1_cartesian.html#a9f51fd4fa6aad2c318df86588ed6a34f">z</a>) * <a class="code hl_variable" href="namespacenc_1_1constants.html#a2f1219a120c9cc1434486d9de75a8221">constants::pi</a> / 2.;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>            alt = <a class="code hl_function" href="namespacenc.html#a6c2c40c4efcd5018f84f9aca0c03c29d">std::abs</a>(ecef.<a class="code hl_variable" href="classnc_1_1coordinates_1_1_cartesian.html#a9f51fd4fa6aad2c318df86588ed6a34f">z</a>) - <a class="code hl_variable" href="namespacenc_1_1coordinates_1_1reference__frames_1_1constants.html#ac759daa1c17c9d6cc404787d56b115ac">reference_frames::constants::EARTH_POLAR_RADIUS</a>;</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        }</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="keywordflow">else</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        {</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>            <span class="comment">// Iteratively update latitude and altitude.</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>            <span class="comment">// This is expected to converge in ~4 iterations, but apply a maximum number of iterations incase tol is</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>            <span class="comment">// too small</span></div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>            <span class="keywordtype">double</span> err  = 1.0;</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>            <span class="keywordtype">int</span>    iter = 0;</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>            <span class="keywordflow">while</span> (err &gt; tol &amp;&amp; iter &lt; MAX_ITER)</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>            {</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>                <span class="keywordtype">double</span> N = <a class="code hl_variable" href="namespacenc_1_1coordinates_1_1reference__frames_1_1constants.html#ace19ddeea3737fe42ad60256f310feaa">reference_frames::constants::EARTH_EQUATORIAL_RADIUS</a> /</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>                           <a class="code hl_function" href="namespacenc.html#a941a5a1ffb61387495a6f23dc4036287">std::sqrt</a>(1 - E_SQR * <a class="code hl_function" href="namespacenc_1_1utils.html#ae792e10a24b7e5b8291a6c31a28a4512">utils::sqr</a>(<a class="code hl_function" href="namespacenc.html#a3fa4e582cdeef0716309ad51378f2983">std::sin</a>(lat)));</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>                lat           = std::atan((ecef.<a class="code hl_variable" href="classnc_1_1coordinates_1_1_cartesian.html#a9f51fd4fa6aad2c318df86588ed6a34f">z</a> / p) / (1 - (N * E_SQR / (N + alt))));</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>                <span class="keywordtype">double</span> newAlt = (p / <a class="code hl_function" href="namespacenc.html#a736de91eb8f79bfaf4dc92d7161f1c87">std::cos</a>(lat)) - N;</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>                err           = <a class="code hl_function" href="namespacenc.html#a6c2c40c4efcd5018f84f9aca0c03c29d">std::abs</a>(alt - newAlt);</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>                alt           = newAlt;</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>                iter++;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>            }</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        }</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>        <span class="keywordflow">return</span> { lat, lon, alt };</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    }</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>} <span class="comment">// namespace nc::coordinates::transforms</span></div>
<div class="ttc" id="a_coordinates_2_reference_frames_2_constants_8hpp_html"><div class="ttname"><a href="_coordinates_2_reference_frames_2_constants_8hpp.html">Constants.hpp</a></div></div>
<div class="ttc" id="a_core_2_constants_8hpp_html"><div class="ttname"><a href="_core_2_constants_8hpp.html">Constants.hpp</a></div></div>
<div class="ttc" id="a_e_c_e_f_8hpp_html"><div class="ttname"><a href="_e_c_e_f_8hpp.html">ECEF.hpp</a></div></div>
<div class="ttc" id="a_l_l_a_8hpp_html"><div class="ttname"><a href="_l_l_a_8hpp.html">LLA.hpp</a></div></div>
<div class="ttc" id="aclassnc_1_1coordinates_1_1_cartesian_html_a9f51fd4fa6aad2c318df86588ed6a34f"><div class="ttname"><a href="classnc_1_1coordinates_1_1_cartesian.html#a9f51fd4fa6aad2c318df86588ed6a34f">nc::coordinates::Cartesian::z</a></div><div class="ttdeci">double z</div><div class="ttdef"><b>Definition:</b> Cartesian.hpp:49</div></div>
<div class="ttc" id="aclassnc_1_1coordinates_1_1_cartesian_html_ac77a08a542ba4d873c0a86047b25953d"><div class="ttname"><a href="classnc_1_1coordinates_1_1_cartesian.html#ac77a08a542ba4d873c0a86047b25953d">nc::coordinates::Cartesian::y</a></div><div class="ttdeci">double y</div><div class="ttdef"><b>Definition:</b> Cartesian.hpp:48</div></div>
<div class="ttc" id="aclassnc_1_1coordinates_1_1_cartesian_html_add44d8cd4ee04ef61120fc0c0d12e550"><div class="ttname"><a href="classnc_1_1coordinates_1_1_cartesian.html#add44d8cd4ee04ef61120fc0c0d12e550">nc::coordinates::Cartesian::x</a></div><div class="ttdeci">double x</div><div class="ttdef"><b>Definition:</b> Cartesian.hpp:47</div></div>
<div class="ttc" id="aclassnc_1_1coordinates_1_1reference__frames_1_1_e_c_e_f_html"><div class="ttname"><a href="classnc_1_1coordinates_1_1reference__frames_1_1_e_c_e_f.html">nc::coordinates::reference_frames::ECEF</a></div><div class="ttdoc">ECEF coordinates.</div><div class="ttdef"><b>Definition:</b> ECEF.hpp:40</div></div>
<div class="ttc" id="aclassnc_1_1coordinates_1_1reference__frames_1_1_l_l_a_html"><div class="ttname"><a href="classnc_1_1coordinates_1_1reference__frames_1_1_l_l_a.html">nc::coordinates::reference_frames::LLA</a></div><div class="ttdoc">Geodetic coordinates.</div><div class="ttdef"><b>Definition:</b> LLA.hpp:40</div></div>
<div class="ttc" id="anamespacenc_1_1constants_html_a2f1219a120c9cc1434486d9de75a8221"><div class="ttname"><a href="namespacenc_1_1constants.html#a2f1219a120c9cc1434486d9de75a8221">nc::constants::pi</a></div><div class="ttdeci">constexpr double pi</div><div class="ttdoc">Pi.</div><div class="ttdef"><b>Definition:</b> Core/Constants.hpp:39</div></div>
<div class="ttc" id="anamespacenc_1_1constants_html_aebabe96d6c2be3df3d71922b399e24c7"><div class="ttname"><a href="namespacenc_1_1constants.html#aebabe96d6c2be3df3d71922b399e24c7">nc::constants::e</a></div><div class="ttdeci">constexpr double e</div><div class="ttdoc">eulers number</div><div class="ttdef"><b>Definition:</b> Core/Constants.hpp:37</div></div>
<div class="ttc" id="anamespacenc_1_1coordinates_1_1reference__frames_1_1constants_html_ac759daa1c17c9d6cc404787d56b115ac"><div class="ttname"><a href="namespacenc_1_1coordinates_1_1reference__frames_1_1constants.html#ac759daa1c17c9d6cc404787d56b115ac">nc::coordinates::reference_frames::constants::EARTH_POLAR_RADIUS</a></div><div class="ttdeci">constexpr double EARTH_POLAR_RADIUS</div><div class="ttdef"><b>Definition:</b> Coordinates/ReferenceFrames/Constants.hpp:33</div></div>
<div class="ttc" id="anamespacenc_1_1coordinates_1_1reference__frames_1_1constants_html_ace19ddeea3737fe42ad60256f310feaa"><div class="ttname"><a href="namespacenc_1_1coordinates_1_1reference__frames_1_1constants.html#ace19ddeea3737fe42ad60256f310feaa">nc::coordinates::reference_frames::constants::EARTH_EQUATORIAL_RADIUS</a></div><div class="ttdeci">constexpr double EARTH_EQUATORIAL_RADIUS</div><div class="ttdef"><b>Definition:</b> Coordinates/ReferenceFrames/Constants.hpp:34</div></div>
<div class="ttc" id="anamespacenc_1_1coordinates_1_1transforms_html"><div class="ttname"><a href="namespacenc_1_1coordinates_1_1transforms.html">nc::coordinates::transforms</a></div><div class="ttdef"><b>Definition:</b> AERtoECEF.hpp:38</div></div>
<div class="ttc" id="anamespacenc_1_1coordinates_1_1transforms_html_ae5b0b317df7fc82c1a6467aa14ac37d4"><div class="ttname"><a href="namespacenc_1_1coordinates_1_1transforms.html#ae5b0b317df7fc82c1a6467aa14ac37d4">nc::coordinates::transforms::ECEFtoLLA</a></div><div class="ttdeci">reference_frames::LLA ECEFtoLLA(const reference_frames::ECEF &amp;ecef, double tol=1e-8) noexcept</div><div class="ttdoc">Converts ECEF coordinates to LLA https://en.wikipedia.org/wiki/Geographic_coordinate_conversion#From_...</div><div class="ttdef"><b>Definition:</b> ECEFtoLLA.hpp:49</div></div>
<div class="ttc" id="anamespacenc_1_1utils_html_ae792e10a24b7e5b8291a6c31a28a4512"><div class="ttname"><a href="namespacenc_1_1utils.html#ae792e10a24b7e5b8291a6c31a28a4512">nc::utils::sqr</a></div><div class="ttdeci">constexpr dtype sqr(dtype inValue) noexcept</div><div class="ttdef"><b>Definition:</b> sqr.hpp:42</div></div>
<div class="ttc" id="anamespacenc_html_a3fa4e582cdeef0716309ad51378f2983"><div class="ttname"><a href="namespacenc.html#a3fa4e582cdeef0716309ad51378f2983">nc::sin</a></div><div class="ttdeci">auto sin(dtype inValue) noexcept</div><div class="ttdef"><b>Definition:</b> sin.hpp:49</div></div>
<div class="ttc" id="anamespacenc_html_a4648674053cd83851d9549bbcc7a8481"><div class="ttname"><a href="namespacenc.html#a4648674053cd83851d9549bbcc7a8481">nc::hypot</a></div><div class="ttdeci">double hypot(dtype inValue1, dtype inValue2) noexcept</div><div class="ttdef"><b>Definition:</b> hypot.hpp:56</div></div>
<div class="ttc" id="anamespacenc_html_a4a5d98f334e0b50a3cf9c2718485e5e9"><div class="ttname"><a href="namespacenc.html#a4a5d98f334e0b50a3cf9c2718485e5e9">nc::sign</a></div><div class="ttdeci">int8 sign(dtype inValue) noexcept</div><div class="ttdef"><b>Definition:</b> sign.hpp:52</div></div>
<div class="ttc" id="anamespacenc_html_a6c2c40c4efcd5018f84f9aca0c03c29d"><div class="ttname"><a href="namespacenc.html#a6c2c40c4efcd5018f84f9aca0c03c29d">nc::abs</a></div><div class="ttdeci">auto abs(dtype inValue) noexcept</div><div class="ttdef"><b>Definition:</b> abs.hpp:49</div></div>
<div class="ttc" id="anamespacenc_html_a736de91eb8f79bfaf4dc92d7161f1c87"><div class="ttname"><a href="namespacenc.html#a736de91eb8f79bfaf4dc92d7161f1c87">nc::cos</a></div><div class="ttdeci">auto cos(dtype inValue) noexcept</div><div class="ttdef"><b>Definition:</b> cos.hpp:49</div></div>
<div class="ttc" id="anamespacenc_html_a941a5a1ffb61387495a6f23dc4036287"><div class="ttname"><a href="namespacenc.html#a941a5a1ffb61387495a6f23dc4036287">nc::sqrt</a></div><div class="ttdeci">auto sqrt(dtype inValue) noexcept</div><div class="ttdef"><b>Definition:</b> sqrt.hpp:48</div></div>
<div class="ttc" id="asign_8hpp_html"><div class="ttname"><a href="sign_8hpp.html">sign.hpp</a></div></div>
<div class="ttc" id="asqr_8hpp_html"><div class="ttname"><a href="sqr_8hpp.html">sqr.hpp</a></div></div>
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